Psych 230 Psychological Measurement and StatisticsToday….A scientific questionHow do we answer this question?Slide 5Hypothesis TestingSlide 7Hypothesis Testing - ExperimentSlide 9Designing the Experiment/StudySlide 11Height - SampleOur DataSlide 14Statistical HypothesesSlide 16Slide 17Slide 18Slide 19Slide 20Z-TestAssumptions of the Z-TestSlide 23Deciding the size of the rejection regionOne-tail versus two-tail testingRejection regionSlide 27Slide 28Rejection region - ExperimentSlide 30Slide 31The obtained and critical valueCalculate the critical valueZcritCalculate the obtained valueSlide 36Zcrit and ZobtSlide 38Drawing a conclusionSlide 40Drawing a different conclusionSlide 42Slide 43Z scores and p valuesTypes of Statistical ErrorType 1 ErrorType 2 ErrorProblem 1Slide 49Slide 50Slide 51Slide 52Slide 53Slide 54Slide 55Slide 56Slide 57Slide 58Slide 59Slide 60Problem 1(b)Slide 62Slide 63Problem 2Slide 65Slide 66Slide 67Slide 68Slide 69Slide 70Slide 71Slide 72Slide 73Slide 74Slide 75Slide 76Problem 3Slide 78Slide 79Slide 80Slide 81Slide 82Slide 83Slide 84Slide 85Slide 86Slide 87Slide 88Slide 89Psych 230Psychological Measurement and StatisticsPedro WolfOctober 21, 2009Today….•Hypothesis testing•Null and Alternative Hypotheses•Z-test•Significant and Nonsignificant results•Types of Statistical error (type 1 and type 2)A scientific question•A biology professor studies the effect of nutrition on physical attributes. He theorizes that maternal nutrition can affect the height and weight of their offspring. Further, he thinks that the time of year a child is conceived, due to seasonal nutrition factors, has a relationship with how tall that child will be. After study, he establishes that yearly nutrition is most different from the norm in June. So, he wants to know whether people conceived in June are a different height than the population.How do we answer this question?1. State the hypotheses2. Design the experiment 3. Collect the data4. Create the statistical hypotheses5. Select the appropriate statistical test6. Decide the size of the rejection region (value of )7. Calculate the obtained and critical values8. Make our conclusionHow do we answer this question?1. State the hypotheses2. Design the experiment 3. Collect the data4. Create the statistical hypotheses5. Select the appropriate statistical test6. Decide the size of the rejection region (value of )7. Calculate the obtained and critical values8. Make our conclusionHypothesis Testing•Experimental hypotheses describe the predicted outcome we may or may not find in an experiment•As scientists, we try to be conservative–we should assume no effect of what we are observing or testing•Does Prozac work in treating depression?•Are men better at math than women?•Do we learn better when practice is all at once or spread over time?Hypothesis Testing•In experiments, we usually identify two hypotheses•The Null Hypothesis (H0)–there is no difference in the groups we are testing•The Alternative Hypothesis (H1)–there is a real difference in the groups we are testingHypothesis Testing - Experiment•The Null Hypothesis (H0)–there is no difference in the groups we are testing•H0 : People born in March are the same height those born in other months•The Alternative Hypothesis–there is a real difference in the groups we are testing•H1 : People born in March are not the same height as those born in other monthsHow do we answer this question?1. State the hypotheses2. Design the experiment 3. Collect the data4. Create the statistical hypotheses5. Select the appropriate statistical test6. Decide the size of the rejection region (value of )7. Calculate the obtained and critical values8. Make our conclusionDesigning the Experiment/Study•Dependent/Observed Variable?•We want to measure height•Independent/Predictor Variable?•Month of birth•March vs all other months•Observational or Experimental study?How do we answer this question?1. State the hypotheses2. Design the experiment 3. Collect the data 4. Create the statistical hypotheses5. Select the appropriate statistical test6. Decide the size of the rejection region (value of )7. Calculate the obtained and critical values8. Make our conclusionHeight - Sample•Heights of those born in March:63, 64, 62, 67, 68, 66, 72, 64•Calculate the mean and standard deviation: X = 65.75SX = 3.03Our DataPopulation = 66.57x = 4.091Sample•N = 8•X = 65.75•SX = 3.03How do we answer this question?1. State the hypotheses2. Design the experiment 3. Collect the data 4. Create the statistical hypotheses5. Select the appropriate statistical test6. Decide the size of the rejection region (value of )7. Calculate the obtained and critical values8. Make our conclusionStatistical Hypotheses•Our hypotheses were:–H0 : People born in March are the same height as those born in other months–H1 : People born in March are not the same height as those born in other months•H0 :  = X•H1 :  ≠ XStatistical Hypothesesa a aa•H0 :  = XStatistical Hypothesesa a aa•H0 :  = XXStatistical Hypothesesa a aa•H1 :  ≠ XStatistical Hypothesesa a aa•H1 :  ≠ XXHow do we answer this question?1. State the hypotheses2. Design the experiment 3. Collect the data 4. Create the statistical hypotheses5. Select the appropriate statistical test6. Decide the size of the rejection region (value of )7. Calculate the obtained and critical values8. Make our conclusionZ-Test•The z-test is the procedure for computing a z-score for a sample mean on the sampling distribution of means•Comparing a sample to a populationAssumptions of the Z-Test•We have randomly selected one sample•The dependent variable is at least approximately normally distributed in the population and involves an interval or ratio scale•We know the mean of the population of raw scores •We know the true standard deviation of the populationHow do we answer this question?1. State the hypotheses2. Design the experiment 3. Collect the data 4. Create the statistical hypotheses5. Select the appropriate statistical test6. Decide the size of the rejection region (value of )7. Calculate the obtained and critical values8. Make our conclusionDeciding the size of the rejection region•Usually, Psychologists use a rejection region of 0.05–known as  (alpha)–sometimes use 0.01 or 0.001–If the H0 is true, the probability of getting an xbar this extreme is